A268776 - OEIS

%I #8 Jan 15 2019 09:10:26

%S 7,26,91,316,1031,3354,10615,33344,103339,317958,970515,2945172,

%T 8888719,26705714,79909167,238257768,708129267,2098664158,6203795403,

%U 18296271036,53845375703,158159174410,463734769895,1357486034320,3967761581627

%N Number of n X 3 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once.

%H R. H. Hardin, <a href="/A268776/b268776.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 16*a(n-3) - a(n-4) + 12*a(n-5) - 4*a(n-6).

%F Empirical g.f.: x*(7 - 2*x - 27*x^2 + 12*x^3 + 8*x^4 - 4*x^5) / (1 - 2*x - 3*x^2 + 2*x^3)^2. -  _Colin Barker_, Jan 15 2019

%e Some solutions for n=4:

%e ..0..1..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..1..0

%e ..0..1..0. .0..1..1. .1..0..0. .0..0..0. .0..0..1. .0..1..0. .0..1..0

%e ..0..0..0. .0..0..0. .0..0..1. .0..0..1. .1..0..0. .0..0..0. .0..0..0

%e ..0..1..0. .0..1..0. .0..1..0. .1..0..0. .1..0..0. .0..0..1. .1..0..0

%Y Column 3 of A268781.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 13 2016